I surprised that loopy was the first one to bring up the possibly biggest factor. Google can't index Flash content. The hit on SEO and Google rankings for having pretty much all of your content go un-indexed is a huge drawback, and should be a giant red flag for any photographer who is pro, semi-pro or hoping to be pro. Unless you are Chase Jarvis, and the whole world already knows who you are and will search for you by name, then everything you can do to get yourself higher on searches is not enough.
But then again, I guess this whole topic has two very different answers based on something that hasn't been clarified yet. Are you trying to make a living from photography, or is it just a hobby? If it's just a hobby and you just want to share your images with people, then who cares what you do. If some people can't see your site, and never come back, it's no big loss.
But if you're trying to make a living from photography, it's foolish to turn away from such a large chunk of the market. Blah blah blah, the Droid is great. Fine it's great, I don't care. TONS of people still have iPhones, and a growing number of people are using iPad as their primary web surfing device. I have an iPhone and an iPad, and I do more surfing on the two of them than I do on my laptop. And when I come to a website that is flash-based an won't open on my iPad, I close it and never go back. I'm not going to go fire up my laptop so I can go look at some site.
In the circles I travel in, which is mostly professional editorial/commercial photographers, photo editors, art directors, and other media professionals, the Apple world dominates everything else by about 2:1. The vast majority of people have iPhones, and many of them have an iPad. It would be downright stupid for me to cut them off from my website and make it so they can only view it at their desk.
Twiter and Facebook are without a doubt the two leading ways in which information and web content are shared these days, and many people are now doing the majority of their social networking on mobile devices. That means that when someone I follow tweets, "Hey, check out this great photographer", and I try to go check them out and get a lank page because it's a flash page, guess what? I'm not looking at it, and I'm never going to. Not because I don't care, but because I can't. And even if I care enough to want to check it later, I'll probably forget. Links are so frequently shared these days, that you have to fight hard for people's attention. Anything you do to make it harder for people to view your site, will result in them navigating away and not coming back.
This isn't about whether the iPhone or Droid is better. No one cares. I love how it used to be cool to have an iPhone and think you were better than everyone else. But then too many people got iPhone, and now it's cool to have not an iPhone and think you're cooler than anyone that has one. Some people are just always looking for a reason to be a part of the elite minority that gets to think they're better than everyone else.
The bottom line is that if you are trying to make a living from photography, then you simply can't afford to build a website that cuts so many people off from viewing it.